Volterra second-order integro-differential equations unresolved for the higher derivative. The case of semibounded operator coefficients.

The theorems of existence and uniqueness of strong solutions to Volterra second-order integrodifferential equations in a Hilbert space are proved in the case where the energy pumping to a system occurs (the energy dissipation operator is bounded from below), and the system can be unstable (the potential energy operator is bounded from below as well). [ABSTRACT FROM AUTHOR]